Just had a close look at what Bronson has to say, and I find his conjectural connection to Corpus Christie extremely weak. For a start the phrase 'His hounds they lie down at his feet' is surely a commonplace that occurs in other ballads. The hounds protecting their slain master, what else should they do, have a dance or sing some dirges? Bronson is presumably irreproachable on the relationship of tunes, but I'm not impressed with his evolution and history of the ballads.
His further point re the hounds licking the wounds in Corpus Christie, his leman KISSES his wounds, hardly comparable. Very week conjecture. IMHO.